HZNUACM寒假集训Day8小结 最小生成树

最小生成树（无向图）

   Kruskal   

   给所有边按从小到大排序 形成环则不选择（利用并查集）

   P1546 最短网络   https://www.luogu.com.cn/problem/P1546

   

#include<iostream>
#include<cstdio>
#include<string>
#include<algorithm>
typedef long long ll;
using namespace std;

struct Node {
    int x, y, w;
    friend bool operator < (const Node& a, const Node& b) {
        return a.w < b.w;
    }
};

Node a[200002];
int pre[200002];

int Find(int x) {
    return pre[x] == x ? x : pre[x] = Find(pre[x]);
}

int main() {
    int n, k, cnt = 0;
    scanf("%d", &n);
    for (int i = 0; i < n; i++) {
        pre[i] = i;
        for(int j=0;j<n;j++){
        scanf("%d", &k);
          if (j > i) {   //矩阵只需判断一半
              a[cnt].x = i;
              a[cnt].y = j;
              a[cnt++].w = k;
          }
        }
    }
    sort(a, a + cnt);
    int ans = 0;
    int p = 0;
    for (int i = 0; i <cnt; i++) {
        if (Find(a[i].x) != Find(a[i].y)) {
            ans += a[i].w;
            pre[Find(a[i].x)] = a[i].y;
            p++;
            if (p == n - 1) break;
        }
    }
    printf("%d\n", ans);
    return 0;
}

    HDU 1875 http://acm.hdu.edu.cn/showproblem.php?pid=1875

   

#include<iostream>
#include<cstdio>
#include<string>
#include<algorithm>
typedef long long ll;
using namespace std;

struct Node {
    int x, y;
    double w;
    friend bool operator < (const Node& a, const Node& b) {
        return a.w < b.w;
    }
};

Node a[6000];    //数组注意开大
int pre[105];
double x[105];
double y[105];

int Find(int x) {
    return pre[x] == x ? x : pre[x] = Find(pre[x]);
}

double dis(double x1, double y1, double x2, double y2) {
    return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
int main() {
    int T,c;
    scanf("%d", &T);
    while (T--) {
        int cnt = 0;
        scanf("%d", &c);
        for (int i = 0; i < c; i++) {
            pre[i] = i;
            scanf("%lf%lf", &x[i], &y[i]);
            for (int j = 0; j < i; j++) {
                double dist = dis(x[i], y[i], x[j], y[j]);
                if(dist>=10.0&&dist<=1000.0){
                a[cnt].x = i;
                a[cnt].y = j;
                //printf("%d %d\n", a[cnt].x, a[cnt].y);
                a[cnt++].w = dist;}
            }
        }
        sort(a, a + cnt);
        double ans = 0;
        int p = 0;
        for (int i = 0; i < cnt; i++) {
            if (Find(a[i].x) != Find(a[i].y)) {
                ans += a[i].w ;
                pre[Find(a[i].x)] = a[i].y;
                p++;
                if (p == c - 1) break;
            }
        }
        if (p == c - 1) printf("%.1f\n", ans*100);
        else printf("oh!\n");
    }
    return 0;
}